Quantum inverse scattering method and correlation functions

By: Korepin, V. E. (Vladimir E.)Contributor(s): Bogoli︠u︡bov, N. M | Izergin, A. GSeries: Cambridge Monographs on Mathematical PhysicsPublication details: Cambridge, U.K.: Cambridge University Press, [c1997]Description: 576 pISBN: 9780521586467Subject(s): Quantum field theory | Inverse scattering transform | Correlation (Statistics)LOC classification: QC174.45 .K67
Contents:
Preface. Part - I (The Coordinate Bethe Ansatz) 1. One-dimensional Bose-gas 2. One-dimensional Heisenberg magnet 3. Massive Thirring model 4. Hubbard model Part - II (The Quantum Inverse Scattering Method) 5. Classical r-matrix 6. Fundamentals of inverse scattering method 7. Algebraic Bethe ansatz 8. Quantum field theory integral models on a lattice Part - III (The Determinant Representation for Quantum Correlation functions) 9. Scalar products 10. Norms of bethe wave functions 11. Correlation functions of currents 12. Correlation functions of fields Part - 4 (Differential Equations for Quantum Correlation functions) 13. Correlation functions for impenetrable Bosons. The determinant representation 14. Differential equations for correlation functions 15. Matrix Riemann-Hilbert problem for correlation functions 16. Asymptotics of Temperature-dependent correlation functions for the impenetrable Bose Gas 17. Algebraic Bethe Ansatz and Asymptotics of correlation functions 18. Asymptotics of correlation functions and the conformal approach. Final Conclusion. References. Index.
Summary: The quantum inverse scattering method is a means of finding exact solutions of two-dimensional models in quantum field theory and statistical physics (such as the sine-Gordon equation or the quantum non-linear Schrödinger equation). These models are the subject of much attention amongst physicists and mathematicians. The present work is an introduction to this important and exciting area. It consists of four parts. The first deals with the Bethe ansatz and calculation of physical quantities. The authors then tackle the theory of the quantum inverse scattering method before applying it in the second half of the book to the calculation of correlation functions. This is one of the most important applications of the method and the authors have made significant contributions to the area. Here they describe some of the most recent and general approaches and include some new results. The book will be essential reading for all mathematical physicists working in field theory and statistical physics.--- Summary provided by the publisher
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Physics Rack No 11 QC174.45 .K67 (Browse shelf (Opens below)) Checked out to Tamoghna Ray (0009040304) 12/09/2024 02841
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Preface.

Part - I (The Coordinate Bethe Ansatz)

1. One-dimensional Bose-gas
2. One-dimensional Heisenberg magnet
3. Massive Thirring model
4. Hubbard model

Part - II (The Quantum Inverse Scattering Method)

5. Classical r-matrix
6. Fundamentals of inverse scattering method
7. Algebraic Bethe ansatz
8. Quantum field theory integral models on a lattice

Part - III (The Determinant Representation for Quantum Correlation functions)

9. Scalar products
10. Norms of bethe wave functions
11. Correlation functions of currents
12. Correlation functions of fields

Part - 4 (Differential Equations for Quantum Correlation functions)

13. Correlation functions for impenetrable Bosons.
The determinant representation
14. Differential equations for correlation functions
15. Matrix Riemann-Hilbert problem for correlation functions
16. Asymptotics of Temperature-dependent correlation functions for the impenetrable Bose Gas
17. Algebraic Bethe Ansatz and Asymptotics of correlation functions
18. Asymptotics of correlation functions and the conformal approach.

Final Conclusion.
References.
Index.

The quantum inverse scattering method is a means of finding exact solutions of two-dimensional models in quantum field theory and statistical physics (such as the sine-Gordon equation or the quantum non-linear Schrödinger equation). These models are the subject of much attention amongst physicists and mathematicians. The present work is an introduction to this important and exciting area. It consists of four parts. The first deals with the Bethe ansatz and calculation of physical quantities. The authors then tackle the theory of the quantum inverse scattering method before applying it in the second half of the book to the calculation of correlation functions. This is one of the most important applications of the method and the authors have made significant contributions to the area. Here they describe some of the most recent and general approaches and include some new results. The book will be essential reading for all mathematical physicists working in field theory and statistical physics.--- Summary provided by the publisher

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